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Monetary innovations, capital taxation, and real wage movements: some new evidence.

I. Introduction

Central to many new classical macroeconomic models is the notion that unanticipated money growth affects real wages adversely while anticipated money growth is neutral. To date, however, the empirical evidence on the subject has been mixed. Early studies of Sargent and Sims |29~ and Sims |30~ reported that monetary surprises had a positive effect on real wages. Leiderman |18~, however, provided evidence consistent with the implications of these models. The results of more recent studies have also been ambiguous. Koray |16~ concludes that anticipated money growth has an adverse effect on total real wages but unanticipated money growth is neutral. In contrast, Kim |15~ finds that both anticipated and unanticipated money growth have negative effects on real wages.

One difficulty with these studies is the implicit assumption that real wage movements are primarily caused by aggregate demand disturbances. In a recent paper, Sumner and Silver |33~ assert that real shocks can also have an important influence on real wages and should be taken into account.(1)

The primary objective of this paper is to re-examine the response of real wages to economic fundamentals within the context of natural-rate new classical equilibrium and contracting models. This paper differs from the existing literature in that we develop a more sophisticated specification for the natural rate component of real wages. Specifically, we model the natural rate in terms of three supply-side disturbances: real energy prices, sector-specific disturbances, and federal policies toward the taxation of capital.

Oil price and sectoral disturbances have previously been incorporated into several studies of output and employment determination. A number of studies have shown that changes in real oil prices have a significant effect on output and employment |10; 11; 23~, the level of manufacturing real wages |18; 33~, and total real wages |16~. It has also been demonstrated that sector-specific disturbances will have adverse effects on economic activity even within the context of flexible-price rational expectations models |19; 4~.(2)

We are not aware of any empirical study that acknowledges an explicit role for capital taxation in determining real wages. However, recent simulation studies have demonstrated that, under plausible assumptions about production technology and wage elasticity of labor supply, replacing a tax on capital income with an equal-revenue-yielding tax on either labor or consumption will substantially accelerate the rate of capital accumulation |2; 13; 21; 32~. This implies that the effective tax rate on capital may have considerable influence on the natural rate component of real wages.

This work differs from the existing literature in two other ways. First, we assess the relative importance of real versus monetary disturbances in explaining real wage behavior. Second, we apply our model to both annual and quarterly data over the 1955-89 period. The more recent time period is especially important for assessing the role of supply-side factors since (i) real oil prices declined precipitously only after 1986 and (ii) federal government policies towards taxation of capital underwent several significant changes during the 1980s.(3)

Our empirical results suggest that once we account for the influence of real shocks, the behavior of real wages is not inconsistent with the predictions of the simple natural-rate macro-models. More specifically, anticipated money growth is neutral while unanticipated money growth has a negative effect on real wages. However, monetary shocks can explain only a small portion of the movements in real wages. Most of the real wage movements over the last twenty years are attributable to supply shocks, especially to changes in federal government policies towards the taxation of capital and changes in real oil prices.

The remainder of this paper is organized as follows. Section II develops the empirical specification of the real wage model. Section III specifies the money growth equation and decomposes money growth into anticipated and unanticipated components. Section IV discusses econometric issues, data, and empirical results. Section V reports the results of simulating the model and section VI contains our summary and conclusions.

II. The Model

The wage equation formulated in this study is in the tradition of the new classical rational expectations equilibrium |20~ and contracting |8; 9~ models. The deviation of the real wage from its natural level is expressed in terms of a finite distributed lag of one-step-ahead errors in predicting money growth,

|Mathematical Expression Omitted~,

where |w.sub.t~ and |Mathematical Expression Omitted~ are logarithms of the actual and natural real wage at time t and |m.sub.t~ and |Mathematical Expression Omitted~ are the actual and anticipated one-step-ahead growth in money supply. We assume that expectations are rational and equal to the conditional forecast of |m.sub.t~ given information available at time t - 1; that is |Mathematical Expression Omitted~. Finally, ||Epsilon~.sub.1t~ is a zero mean (possibly serially correlated) error.

Traditionally, the natural component of real wages has been modeled as a deterministic trend. For example, Leiderman |18~, Koray |16~, and Sumner and Silver |33~ account for the movement in the natural rate using a time trend and a proxy for real oil price shocks. This approach to modeling the natural rate is problematic on at least two grounds. First, several factors in addition to oil shocks may exert a significant effect on the natural levels of economic activity |7~. Second, there is substantial evidence that natural real wages are best approximated by a stochastic model |26; 31~.(4)

We address these problems by allowing three real factors--capital taxation, real oil prices, and sector-specific disturbances--to affect the natural level of real wages and by modeling real wages as a nonstationary stochastic process. The remainder of this section explains the construction of the three supply-side variables and our approach to modelling the nonstationarity in the real wage series.

Capital Taxation

Measuring the effective tax rate on capital is an inherently difficult task |32~. We proxy this variable by a measure of the effective federal tax rate on corporate income. This measure, |TK.sub.t~, is constructed from national income accounts data following the methodology of Amerkhail, Spooner, and Sunley |1~.(5) That is,

|TK.sub.t~ = (|CT.sub.t~ - |FRP.sub.t~)/(|CP.sub.t~ - |PFRB.sub.t~), (2)

where CT is corporate profit tax accruals, FRP is Federal Reserve payments, CP is corporate profits with inventory valuation and capital consumption adjustment, and PFRB is profits of the Federal Reserve banks. This measure accounts for the influence of inflation as well as statutory changes in corporate income tax laws.(6)

Real Oil Prices

In constructing an index of oil prices we adopt the procedure suggested by Mork |23~ of supplementing data on the producer price of crude oil with data on refiner acquisition cost (composite domestic and imported) for the post- 1970 oil price control period. Our measure of the real price of energy, |Poil.sub.t~, is the natural logarithm of the constructed series adjusted by the GNP deflator.(7)

Sector-Specific Disturbances

As have Lilien |19~ and others, we measure the magnitude of sector-specific shocks with |S.sub.t~, an index of the dispersion of one-period employment changes across nineteen two-digit SIC manufacturing classifications. Formally,

|Mathematical Expression Omitted~

where |E.sub.t~ and |E.sub.it~ are total and industry specific levels of employment and |e.sub.t~ and |e.sub.it~ are their respective natural logarithms.

Nonstationarity

In preliminary analysis we conducted tests of a unit root in the real wage series following the methodology proposed by Nelson and Plosser |26~. Our empirical results confirm earlier findings that real wages are most appropriately modeled as a difference stationary process.(8)

We incorporate nonstationarity into our model by following a framework similar to that of Gray and Spencer |10~. In particular, the natural real wage, |Mathematical Expression Omitted~, is modeled as the sum of two processes. The first is explained by the observable real variables |Poil.sub.t~, |S.sub.t~, and |TK.sub.t~. The second, |Mathematical Expression Omitted~, is an unobserved difference stationary process that captures the effects of other nonstationary factors such as capital accumulation and changes in resources and technology.(9) More formally,

|Mathematical Expression Omitted~

where |Mathematical Expression Omitted~.

Substituting equations (4) and (5) into equation (1) and taking the first difference of the resulting equation yields,

|Mathematical Expression Omitted~

where D is the first difference operator and ||Epsilon~.sub.t~ is a linear combination of the current and lagged values of ||Epsilon~.sub.1t~ and ||Epsilon~.sub.2t~ and the current value of ||Epsilon~.sub.3t~.

III. Money Growth Equation

Estimation of the real wage equation developed in the previous section requires proxies for anticipated (|Mathematical Expression Omitted~) and unanticipated (|Mathematical Expression Omitted~) changes in money growth. We assume that expectations of money growth during period t are formed rationally using all available information at time t - 1. As in Mishkin |22~, anticipated money growth is generated using the linear forecasting equation

|m.sub.t~ = |z.sub.t-1~|Theta~ + |u.sub.t~, (7)

where |z.sub.t-1~ is a vector of variables used to forecast money growth, |Theta~ is a vector of coefficients, and |u.sub.t~ is an error term uncorrelated with any information at time t - 1.

Anticipated money growth is obtained by taking the expectation of equation (7) conditional on information available at t - 1,

|Mathematical Expression Omitted~.

In implementing this procedure we incorporate two recent developments in the literature. First, we choose the base money supply as the monetary aggregate as in Rush |27; 28~ and London and Reid |17~.(10) Second, we use the multi-variate Granger causality test and the criterion of minimum final-prediction-error (FPE) in choosing the vector z as in Koray |16~, and Fackler and Parker |6~.

The annual specification of vector z includes two lags of money growth, one lag of the growth of the nominal national debt, the commercial paper rate, the inflation rate, and a dummy variable, DUM, to take into account the effect of the change in the monetary regime after 1979.(11)

In the quarterly specification of vector z we constrained the search process by entering each variable in blocks of four lags and retaining the block if it reduced the FPE of the resulting regression. The final specification includes lagged money growth, the growth rate of nominal national debt, the commercial paper rate, the inflation rate, the log of real government expenditures, and DUM.(12)

IV. Estimation, Data, and Results

The real wage and money growth equations were estimated using annual and quarterly data over the period 1955-1989.(13) To obtain correct inferences and test statistics, cross-equation restrictions were imposed by carrying out the estimation using nonlinear seemingly unrelated regression. Also, we assumed that the residuals in the wage equation follow a first order autoregressive process.

Following the earlier literature we employ four alternative proxies for real wages. These measures are obtained by deflating two nominal wage series, the average hourly earnings per production worker on the payrolls of manufacturing establishments exclusive of overtime (W) and inclusive of overtime (WI), by the Producer Price Index (PPI) and the Consumer Price Index (CPI). These calculations yield two product wage (w1 = W/PPI, w2 = WI/PPI) and two consumption wage (w3 = W/CPI, w4 = WI/CPI) measures.

Annual Results

The results of estimating wage equations using annual data are reported in Table I. Each wage equation contains the current and one lagged values of the capital tax rate, current values of the real oil price and sectoral shocks, and current and three lagged values of unanticipated money growth.(14)

Several interesting results emerge. First, anticipated money growth is neutral as in Leiderman |18~. The chi-square tests for the joint significance of current and three lagged values of anticipated money growth are below the conventional 5 percent critical value of 9.488 in all four wage equations.

Second, unanticipated money growth has a weak yet statistically significant effect on real wages. The test statistics for the joint significance of current and three lagged values of unanticipated money growth are above the critical value in all wage equations. However, the direction of the effects is not identical. Unanticipated money growth has a negative effect on product wages but a positive effect on consumption wages.(15)

Third, the supply-side variables are jointly significant and have a strong effect on all measures of real wages.(16) They are also important determinants of the real wage when considered individually. In particular, the current and first lagged values of the capital tax rate have the expected negative effects and are jointly significant. However, additional lags of this variable are not significant, indicating that the major impact of a change in effective corporate income tax rates occurs within the first two years.(17)

Fourth, changes in real oil prices and sectoral shocks also have an important influence on TABULAR DATA OMITTED real wages. In all wage equations these variables have the expected negative sign, although the effect of real oil prices in the consumption wage equations is relatively weak.(18)

In light of recent theoretical work by Hamilton |12~ we also tested for the possibility of asymmetric response of real wages to oil price shocks. This test was accomplished by decomposing the change in real oil prices into two series of positive (zero otherwise) and negative (zero otherwise) variables. The null hypothesis of symmetry in oil price effects cannot be rejected.(19)

Finally, in contrast to Leiderman |18~, we find no strong evidence for the view that product wage equations systematically outperform consumption wage equations.

Quarterly Results

To gain insight into the dynamics of real wage movements we also estimated quarterly wage equations. The real wage equation is modified to include the current and three lagged values of the sectoral disturbances, real oil prices, the capital tax rate, and the current and eleven lagged values of unanticipated money growth. Also, three dummy variables, D1-D3, are included to account for the effect of seasonal variation in real wages. The quarterly versions of the money growth (discussed in section III) and real wage equations are jointly estimated over the 1955:I-1989:IV sample period. The results are reported in Table II.

TABULAR DATA OMITTED

With a few exceptions, the results are broadly consistent with the findings for the annual wage equations. The most notable differences center on the role of money. Neutrality of anticipated money growth was tested by including the current and eleven lagged values of this variable. The null hypothesis of neutrality was rejected for the consumption but not for the product wage equations. Here, contrary to the annual results, anticipated changes in money growth have a positive effect on consumption real wages.

The evidence on the role of unanticipated money growth on real wages is now similar for both PPI and CPI deflated wage series. For all real wage measures the current and eleven-quarter lags of unanticipated money growth are jointly negative and significant. Viewed as a whole, these results constitute stronger evidence than has been observed heretofore for the proposition that unanticipated changes in money growth affect real wages adversely.

The response of real wages to unanticipated money growth (in absolute value) follows the well-documented inverted "V" pattern. In all four equations the peak effect of unanticipated money on real wages occurs after a lag of seven quarters. Interestingly, our estimate of the peak real wage response is over twice the lag length observed by Leiderman |15~ and Kim |18~.

For the most part the quarterly results support the conclusions drawn from the annual data regarding the role of supply-side variables. The current and three quarter lagged values of the capital tax have a jointly significant and negative effect on real wages, although the evidence is relatively weak for the consumption wage inclusive of overtime. The coefficients of the oil price variables generally have the expected signs and are jointly significant in the product wage equations. Finally, sectoral shocks have a significant effect only on consumption wages.

V. Simulation Results

To gain additional insight into the relative importance of supply shocks, we simulated the partial response of real wages to the actual movements in each factor in the model over the past 35 years. To conserve space, we only report the results for the product wage model using annual data. The solid lines in Figures 1 through 4 represent the deviation of the growth in actual real wages from the 1955 base year. The broken lines depict the partial response of real wage growth to each of the variables.(20)

The change in real wage growth resulting from sectoral shocks is plotted in Figure 1. This figure shows that sector-specific disturbances are a contributing factor behind relatively modest cyclical movements of real wages, such as those occurring in the 1950s and 1960s. This factor, however, explains little of the more dramatic real wage movements that occurred during the latter half of the period under analysis.

In contrast, Figures 2 and 3 reveal that the tax rate on capital and changes in real oil prices played major roles in real wage movements over the past twenty years. For example, these two factors combined explain well over half of the large decline in real wage growth experienced during the mid and late 1970s and again in the late 1980s.

The influence of these two real variables on real wage movements stands in dramatic contrast to the contribution of unanticipated money growth. This demand-side factor explains relatively little of the large swings in real wage growth observed during the 1970s and 1980s.

VI. Conclusions

This paper investigated the determinants of real wages within the context of a model that distinguishes between demand-side and supply-side origins of changes in real activity. We find that once the influence of real shocks on the natural component of real wages is accounted for, the behavior of real wages is not inconsistent with the predictions of natural-rate macro-models. The strongest evidence for the propositions of the simple natural-rate model is found when wages are deflated by the PPI. In such cases, unanticipated money growth consistently has a negative and statistically significant effect on real wages, while anticipated money growth is neutral. Unanticipated money growth, however, can explain only a relatively small portion of the movements in real wages observed during the past twenty years.

Most of the real wage movements during this time can be attributed to supply shocks. In particular, our findings support the supply-side view that federal tax policies regarding investment incentives have an important influence on capital formation and labor productivity. Again, the strongest evidence is obtained when nominal wages are deflated by the producer price index. In this case, incentives such as the investment tax credit and accelerated depreciation have a positive and highly significant influence on real wage behavior. This result suggests that the reversal of investment incentives contained in the Tax Reform Act of 1986 may portend a slowdown in real wage growth in future years.

1. More generally, Gray and Spencer |10~ make a similar argument in their assessment of the recent literature that finds that natural-rate macro-models are of questionable empirical relevance in determining the level of real economic activity.

2. Furthermore, Black |3~, Davis |5~, and Hamilton |12~ have argued that the short-run decline in economic activity is exacerbated if (i) capital is sector specific and (ii) labor requires retraining as it moves into expanding sectors. The latter phenomenon implies that sectoral shocks reduce the marginal productivity of labor and hence real wages in the short-run.

3. Most time-series studies in this area employ data sets that end in 1970s. An exception is Sumner and Silver's |33~ analysis of a 1903-85 period.

4. Nelson and Kang |24; 25~ show that if a series is modeled as a deterministic trend while its true process is difference stationary, then the influence of the long-term determinants will be underestimated.

5. The reader may question restricting TK to include only corporate income taxes. For example, Summers |32~ argues that a capital tax measure should include corporate taxes, individual income taxes on dividends and interest income, and property taxes. Nevertheless, the supply-side perspective typically emphasizes the role of certain tax incentives such as the investment tax credit and accelerated depreciation in the capital formation process |34~. Such incentives, it is argued, can have an immediate and dramatic effect on the level of investment activity. Our measure of capital taxation can be thought of as a proxy for the trend in tax policy regarding such incentives.

6. Except for the inflationary periods of 1973-74 and 1979-80, effective tax rates generally declined over much of the post war era. The decline accelerated in the early 1980s as a result of legislation that permitted faster depreciation of short-term assets. However, this downward trend was sharply reversed after 1985 as a result of tax legislation enacted during the mid-1980s. The most profound changes were the result of 1986 legislation that lengthened the depreciation period for many assets and repealed the investment tax credit, while cutting statutory rates. As a result, effective tax rates on short-term assets rose sharply while rates on long-term assets experienced modest declines.

7. Mork's |23~ paper is of particular interest because his empirical analysis addresses a period (1949-88) when the relative price of oil exhibited periods of substantial decline as well as increase. He finds that changes in relative oil prices have asymmetric effects on economic performance; that is, while oil price increases have a negative influence on the growth in real GNP, oil price decreases have little effect. In the empirical analysis that follows we test for the possibility that changes in real oil prices have asymmetric effects on the natural real wage.

8. These results are available upon request.

9. The variable |Mathematical Expression Omitted~ will also capture the effect on real wages of movements in capital taxation not accounted for by TK, such as the gradual decline in the relative importance of the property tax during the period under analysis. See also note 5.

10. This choice offers important advantages over other measures. It is directly under the control of the monetary authorities, and thus is predetermined |14~. It is also consistent with both monetary and interest rate targeting.

11. The following additional variables were also considered for inclusion in both annual and quarterly money growth equations: the unemployment rate, the rate of change in import price deflator, the growth rates of nominal and real GNP, the real price of petroleum, the rate of change of real federal government expenditures, the real national deficit, the rate of change in real national debt, and the nominal exchange rate.

12. We tested for the stability of both the annual and quarterly specifications of the money growth equation by splitting the sample in approximately half and performing a Chow test. In each case the null hypothesis of stable coefficients was not rejected.

13. The original data set covers the 1947-89 period. However, observations on 1947-54 are lost in the data transformation and lagging process.

14. The structure of the lag lengths is broadly consistent with the institutional features of the labor market and the contracting literature.

15. Although contradictory, these results are consistent with Sumner and Silver's |33~ conclusion from an analysis of annual data over a longer period (1905-1985). They rationalize their findings by arguing that the underlying theory that predicts a countercyclical real wage is based on movements along a stable demand curve for labor and that a PPI-deflated wage is a more appropriate measure of the firm's demand price of labor. Other studies |15; 18~ also find a substantially weaker countercyclical pattern in real wages over monetary business cycles with CPI-deflated wage series.

16. When the real wage equations are estimated without the supply-side variables the coefficients of the unanticipated money growth variables become more negative and their overall statistical significance increases. This indicates that the pattern of real wage movements in response to unanticipated money growth may also depend on the response of monetary authorities to supply shocks. In particular, if monetary policy is accommodating, the omission of the supply-side variables may lead to a countercyclical bias in real wage behavior.

17. This conclusion should be viewed with some caution, however, since TK represents an average effective tax rate on all corporate capital. As previously noted (footnote 6), some of the major changes in this variable occurred in the 1980s and were largely the result of changes in the effective tax rate on machinery and equipment. Thus, our findings may indicate that changes in tax policy regarding short-lived assets affect the marginal productivity of labor within a relatively short period of time.

18. We also investigated the possibility that sector-specific disturbances may be influenced by other variables in the wage equation. This was accomplished by purging S of the effects of contemporaneous values of Poil, TK, and D|m.sup.u~. None of these variables had a statistically significant effect on S in the annual model. Moreover, the overall results for the wage equations were unaltered irrespective of the measure of sector-specific disturbances employed.

19. Interestingly, this finding is in contrast to Mork's |23~ conclusion that oil price shocks have an asymmetric effect on real GNP growth.

20. For example, the partial real wage response at time t to sectoral shocks is calculated as -0.149(|DS.sub.t~ - |DS.sub.1955~). For the tax and unanticipated money variables, the base year is appropriately lagged to account for their lagged influence on real wages.

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2. Auerbach, Alan J., and Laurence J. Kotlikoff. Dynamic Fiscal Policy. Cambridge, England: Cambridge University Press, 1987.

3. Black, Fischer. "General Equilibrium and Business Cycles." Working Paper no. 950. Cambridge, Mass.: NBER, August 1982.

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29. Sargent, Thomas J., and Christopher A. Sims. "Business Cycle Modeling Without Pretending to Have Too Much a priori Economic Theory," in New Methods in Business Cycle Research: Proceedings from a Conference. Minneapolis: Federal Reserve Bank of Minneapolis, 1977.

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32. Summers, Lawrence H., "Capital Taxation and Accumulation in a Life Cycle Growth Model." American Economic Review, September 1981, 533-44.

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34. Tatom, John A., "U.S. Investment in the 1980s: The Real Story," Federal Reserve Bank of St. Louis, March/April 1989, 3-15.
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